Algebra 1 Exponential Functions and Growth Test Solutions and Scoring (PDF)

a) \(b = 1.3 > 1\): growth of 30%.

b) \(b = 0.6 < 1\): decay of 40%.

a) growth, 30%; b) decay, 40%

Scoring: 1 point for each part.

\(f(4) = 5 \cdot 16 = 80\).

\(f(-1) = 5 \cdot 2^{-1} = 5 \cdot \frac{1}{2} = 2.5\).

80; 2.5

Scoring: 1 point for each value.

The starting value is 3 and the ratio is \(\frac{6}{3} = 2\), \(\frac{12}{6} = 2\).

\(y = 3 \cdot 2^{x}\)

Scoring: 1 point for the starting value; 1 point for the factor and equation.

Values: \(6, 3, 1.5, 0.75\). Plot them and draw a smooth decreasing curve.

Scoring: 1 point for correct values; 1 point for a correct curve.

a) \(A = 500(1.08)^{t}\).

b) \(500(1.08)^{3} = 500(1.259712) = 629.856 \approx 629.86\).

\(A = 500(1.08)^{t}\); $629.86

Scoring: 1 point for the model; 1 point for the amount.

a) \(125 = 5^{3}\), so \(x = 3\).

b) \(16 = 2^{4}\), so \(x + 1 = 4\) and \(x = 3\).

x = 3; x = 3

Scoring: 1 point for each part.

a) \(1 – 0.9 = 0.1\): 10% per year.

b) \(30000(0.9)^{4} = 30000(0.6561) = 19683\).

c) After 3 years: \(30000(0.9)^{3} = 21870\). After 4 years: 19,683, which is below 20,000.

10%; $19,683; year 4

Scoring: 1 point per part.

a) Week 5: A has $350 and B has $320, so Plan A.

b) Week 6: A has $400 and B has $640, so Plan B.

c) Plan A adds a fixed $50 each week, but Plan B multiplies by 2, so the amount it adds keeps growing and soon exceeds $50.

Plan A; Plan B; B multiplies

Scoring: 1 point per part.

\(A = 120\left(\frac{1}{2}\right)^{t/4}\).

For \(t = 12\): \(120\left(\frac{1}{2}\right)^{3} = 120 \cdot \frac{1}{8} = 15\).

15 mg

Scoring: 1 point for the model; 1 point for the amount.